Question

A cubical box has each edge 10 cm and a cuboidal box is 5 cm wide, 10 cm long and 6 cm high. Which box has the smaller total surface area ?​
cubical box

cuboidal box

Answer 1

$\huge{\underline{\underline{\bf{\blue{GIVEN:-}}}}}$

• Edge of a cubical box = 10 cm
• Length of the coboidal box = 10 cm
• Breadth of the cuboidal box = 5 cm
• Height of the cuboidal box = 6 cm

$\huge{\underline{\underline{\bf{\blue{TO\:FIND:-}}}}}$

Find the T.S.A. of cubical and cuboidal box and also find which box have smaller surface area = ?

$\huge{\underline{\underline{\bf{\blue{FORMULA\: USED:-}}}}}$

$\large{\boxed{\bf{\red{T.S.A. of cube = 6{a}^{2}}}}}$

$\large{\boxed{\bf{\red{T.S.A. of cuboid = 2(lb + bh + hl)}}}}$

$\huge{\underline{\underline{\bf{\blue{SOLUTION:-}}}}}$

Firstly, we need to find the surface area of cubical box

Putting the values in the formula, we get

$\large\bf{T.S.A. of cube = 6{a}^{2}}$

$\implies$$\bf{T.S.A. = 6{(10)}^{2}}$

$\implies$$\bf{T.S.A. = 6\times 100}$

$\implies$$\large\bf\red{T.S.A. = 600\: {cm}^{2}}$

Thus, the T.S.A. of cubical box is 600 cm²

Now, we have to find the surface area of cubical box

Putting the values in the formula, we get

$\large\bf{T.S.A. of cuboid = 2(lb+bh+hl)}$

$\implies$$\bf{T.S.A. = 2(10 \times 5 + 5 \times 6 + 6 \times 10)}$

$\implies$$\bf{T.S.A. = 2(50 + 30 + 60)}$

$\implies$$\bf{T.S.A. = 2\times 140}$

$\implies$$\large\bf\red{T.S.A. = 280\: {cm}^{2}}$

Thus, the T.S.A. of cuboidal box is 280 cm²

Hence, the Surface area of cuboidal box is smaller..

Answer 2

Given

$\bold{Length \ of \ the \ cube} = 10 \ cm$

$\bold{Length\ of \ the \ cuboid} = 10 \ cm$

$\bold{Width\ of \ the \ cuboid} = 5 \ cm$

$\bold{Height \ of \ the \ cuboid} = 6 \ cm$

SOMETHING YOU NEED TO KNOW

TSA of a cube = 6a²

TSA of a cuboid = 2(lb + bh + hl)

$\implies 6a^{2}\\ \implies 6 * 10*10\\\implies 600 \ cm^{2}\\ \\\boxed{\boxed{\bold{Therefore, \ the \ total \ surface \ area \ of \ the \ cube \ is \ 600 \ cm^{2}}}}}$

$\implies 2(lb+bh+hl)\\\implies 2(10*5+5*6+6*10)\\\implies 2(50+30+60)\\\implies 2(140)\\\implies 280 \ cm^{2} \\\\\boxed{\boxed{\bold{Therefore, \ the \ total \ surface \ area \ of \ the \ cuboid \ is \ 280 \ cm^{2}}}}}$

=> The Cube Has More Surface Area